Digital Image Processing Laboratory: Image Filtering ...

Purdue University: Digital Image Processing Laboratories

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Digital Image Processing Laboratory:

Image Filtering

January 26, 2021

Introduction

In this laboratory, you will filter full color images using both FIR and IIR filters, and you

also will learn to use Python to read, show, and write your images.

In this laboratory assignment, the filter algorithms should be implemented in the C

programming language, unless otherwise stated. Low level programming languages are necessary for implementing many complex image processing operations, so one objective of this

laboratory is to give you some experience in using C to solve image processing problems.

Simple example programs are provided, so you should be able to write the required programs

even if you have very little previous experience with C.

When processing images on a computer, there are usually special cases that must be properly handled. In particular, all filters will be implemented using free boundary conditions

along edges, and pixel values will be clipped to a range of [0, 255].

? Free boundary conditions - In order to understand a free boundary condition, consider

an M ¡Á N image denoted by img(i, j) where 0 ¡Ü i < M and 0 ¡Ü j < N . Some filtering

operations require that you index outside of this valid range. Pixels indexed outside

this range should be considered equal to zero.

? Clipping - Image processing operations will sometimes cause a pixel to exceed the value

255 or go below the value 0. In these cases, you should clip the pixel¡¯s value before

displaying or exporting the image.

?

?

?

0

if x(m, n) < 0

if x(m, n) > 255

y(m, n) = 255

?

?

x(m, n) if 0 ¡Ü x(m, n) ¡Ü 255

Questions or comments concerning this laboratory should be directed to Prof. Charles A. Bouman,

School of Electrical and Computer Engineering, Purdue University, West Lafayette IN 47907; (765) 4940340; bouman@ecn.purdue.edu

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C Programing

An important goal of these laboratories is for you to learn good C programming skills. You

do not need much prior experience in C programming, because the laboratories will lead you

through the use of the language with examples and program templates. However, to learn

good C programming skills, you should strictly follow the following set of rules at all times.

? Use strict ANSI C constructs - All C compilers allow for enforcement of strict

ANSI C. You should use these options at all times. With the gcc compiler under the

Linux operating system, the compiler flags are

gcc -ansi -Wall -pedantic

These flag settings will insure that you receive warnings for any poor programming

constructs in your code.

? Never use global variables - Global variables should never be used. There are

exceptions to this rule, but you will never face a situation where they are truly needed.

Global variable will lead to ¡°spaghetti code¡±, that can not be understood or debugged.

? Fix all compiler warnings - Any warning from the compiler means that you have an

error in you program or are using poor programming style. Either problem is serious

and should be corrected. Typically, warnings are generated when variables are not

properly retyped. The only exception to this rule is when you dynamically allocate

memory. In this case, you may receive a warning about the byte location.

? Use prototypes for all subroutines - Every subroutine you write should have a prototype that defines its argument types. This prototype should generally be contained

in a single header file with a name such as defs.h.

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Displaying and Exporting Images in Python

Most of the lab exercises in this class will require you to produce one or more output images.

These will need to be incorporated into your pdf report. Since many exercises will use

Python, we describe here some basic I/O and display commands in the Python environment.

? Setup Conda Environment - It is recommended that you create a conda environment for this course using the following procedure:

1. Install Anaconda through its website.

2. An ASCII file named ¡°environment.yml¡± is provided that can be used to configure

your Anaconda environment. The file, shown below, installs the packages called

¡°numpy¡±, ¡°matplotlib¡±, and ¡°pillow¡± that will be used in the class.

name : ECE637

dependencies :

? numpy

? matplotlib

? pillow

3. Create the conda environment by running the following command with the file

¡°environment.yml¡± in your working directory.

conda env c r e a t e ?f environment . yml

4. Activate conda environment with the following command.

conda a c t i v a t e ECE637

? Reading Images - You can read an image file, img.tif, into python using pillow using

the following commands

from PIL import Image

im = Image . open ( ¡¯ img . t i f ¡¯ )

This will produce an image matrix x of data type uint8.

? Displaying Images - You can display the image array x with the following command,

im . show ( )

? Transfer Image to numpy array - You can transfer an image object to a numpy

array using the following commands,

import numpy as np

x = np . a r r a y ( im )

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? Writing Images - When producing a lab report document, you should strive to

present the best representation of your output images. Therefore it is best to export

your images to a lossless file format, such as TIFF or BMP, which can then be imported

into your lab report document. You can write the image array x to a file using the save

function:

img out = Image . f r o m a r r a y ( x )

img out . s a v e ( ¡¯ img out . t i f ¡¯ )

Note that if x is of type uint8, the imwrite function assumes a dynamic range of [0,255],

and will clip any values outside that range. If x is of type double, then imwrite assumes

a dynamic range of [0,1], and will linearly scale to the range [0,255], clipping values

outside that range, before writing out the image to a file. To convert the image to type

uint8 before writing, you can use

img out = Image . f r o m a r r a y ( x . a s t y p e ( np . u i n t 8 ) )

img out . s a v e ( ¡¯ img out . t i f ¡¯ )

In most of the following exercises, your C routines will output TIFF files which can be

imported into your lab document. Your lab document should be submitted in pdf (portable

document format), but it can be prepared using an application such as Latex or MS Word.

When you prepare your lab document, you may need to convert the image to an intermediate

format such as jpeg . If you do this, try to set the image quality parameters to the best

possible setting in order to preserve image detail and quality.

For your own viewing, you may display the output images using Python as described

above, or using any other standard image viewing software. Regardless, you are encouraged

to experiment with the effect of each of the above commands using one of the images provided

on the lab web page.

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FIR Low Pass Filter

In this problem, you will analyze and implement a simple low pass filter given by the 9 ¡Á 9

point spread function

(

h(m, n) =

1/81 for |m| ¡Ü 4 and |n| ¡Ü 4

0

otherwise

.

1. Calculate an analytical expression for H(ej? , ej¦Í ), the DSFT of h(m, n), and use

Python¡¯s matplotlib to plot the magnitude of the frequency response |H(ej? , ej¦Í )|.

Make sure to label the axes properly and plot on over the region [?¦Ð, ¦Ð] ¡Á [?¦Ð, ¦Ð].

2. Download the bundle C-code.zip containing the C source code for reading and writing

tagged image file format (TIFF) images. Compile the application Example using an

ANSI C compiler.

3. Run the program Example on the image img03.tif by using the command

Example img03.tif

This will produce the gray scale image green.tif, which is derived from the green component of img03.tif.

4. Modify the program Example so that it filters the red, green and blue components of

img03.tif with the filter h(m, n) and generates a full color output image.

Warning: Make sure to rename the directory containing your modified program so

that it can not be overwritten with the original C-code program directory.

Note: In the example code provided, noise is added to the image before writing it

out. This is for illustration only¨Cyou are not asked to add noise to your image in this

exercise.

5. Include the filtered image in your report.

Section 3 Report:

Hand in:

1. A derivation of the analytical expression for H(ej? , ej¦Í ).

2. A plot of |H(ej? , ej¦Í )|.

3. The color image in img03.tif.

4. The filtered color image.

5. A listing of your C code.

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